Measurement apparatus and exposure apparatus

ABSTRACT

A measurement apparatus which measures spatial coherence in an illuminated plane illuminated by an illumination system, comprises a measurement mask which has at least three pinholes and is arranged on the illuminated plane, a detector configured to detect an interference pattern formed by lights from the at least three pinholes, and a calculator configured to calculate the spatial coherence in the illuminated plane based on a Fourier spectrum obtained by Fourier-transforming the interference pattern detected by the detector.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a measurement apparatus which measuresspatial coherence, and an exposure apparatus including the same.

2. Description of the Related Art

In a lithography process for manufacturing devices such as asemiconductor device, mainly in photolithography, the NA of a projectionoptical system is increasing, and the wavelength of exposure light isshortening in an exposure apparatus. As the NA increases, the resolvingpower improves, but the depth of focus decreases. For this reason, fromthe viewpoint of forming finer patterns than ever before, increasing theNA of the projection optical system alone has proved to be insufficientto sustain stable mass production. Under the circumstances, so-calledmodified illumination methods which improve the resolutioncharacteristics by optimizing an illumination optical system areattracting a great deal of attention.

There is a recent tendency to optimize not only the σ value, that is,the ratio between the NAs of the illumination optical system andprojection optical system but also the effective light source shapes forindividual original patterns. Examples of the modified illumination areannular illumination, quadrupole illumination, and dipole illumination.

However, the optical path changes upon changing the illumination mode,so spatial coherence on the original surface (in the object plane of theprojection optical system) changes due to, for example, unevenness of anantireflection coating of an optical element which constitutes theillumination optical system or decentering of the optical element. Sucha change in spatial coherence has a considerable influence on thequality of an image formed on the image plane of the projection opticalsystem. It is therefore important to know spatial coherence and take itinto consideration in designing an original and determining theeffective light source distribution.

Known spatial coherence measurement methods are the following threemethods. The first method is so-called Young interferometry or a doublepinhole method (Joseph W. Goodman, “Statistical Optics”). The secondmethod is shearing interferometry. The third method is a method ofmeasuring spatial coherence based on a change in a certain patternimage.

FIG. 17 is a view showing the principle of Young interferometry as thefirst method. A plate 61 having two pinholes is irradiated by a lightsource 60, and the light beams from these two pinholes are made tointerfere with each other on a screen 62 set behind the plate 61,thereby calculating spatial coherence based on the contrast of theobtained interference fringes. Japanese Patent Laid-Open No. 7-311094describes an application example of the first method.

FIG. 18 is a view showing the principle of shearing interferometry asthe second method. FIG. 18 schematically shows the structure of aMichelson interferometer. In the Michelson interferometer, when incidentlight 70 strikes a half mirror 71, it is split into a light beam 70 awhich travels toward a reference prism mirror 72 and a light beam 70 bwhich travels toward a movable prism mirror 73. Light beams 70 c and 70d reflected by the respective mirrors 72 and 73 return to the halfmirror 71 and are superposed on each other to form interference fringeson a screen 74.

When the reference prism mirror 72 and the movable prism mirror 73 areplaced such that two light beams which travel toward them have the sameoptical path length, and the movable prism mirror 73 moves in the Y-axisdirection, the reflected light beam 70 d also moves by the same distanceand is superposed on the reflected light beam 70 c. At this time, sincethe contrast of the interference fringes change in correspondence withspatial coherence, the spatial coherence can be measured by observingthe moving distance of the movable prism mirror 73 in the Y-axisdirection, and a change in the contrast of the interference fringes.Japanese Patent Laid-Open No. 9-33357 and Japanese Patent PublicationNo. 6-63868 describe application examples of the second method.

Japanese patent Laid-Open No. 10-260108 describe an example of the thirdmethod. According to Japanese Patent Laid-Open No. 10-260108, spatialcoherence is measured by projecting a rhombic pattern and measuring thesize of the projected image.

Unfortunately, Young interferometry as the first method has a demeritthat the two pinholes need to be replaced a plurality of times to obtainspatial coherences at a plurality of points because the interval betweenthese pinholes is fixed, taking a long period of time. Shearinginterferometry as the second method has a demerit that not only ahigh-precision optical system is necessary but also it is hard to mounta shearing interferometer into an exposure apparatus which hassignificant spatial constraints because of its difficulty in downsizing.The third method is mainly used to measure the σ value (the ratio(NAill/NApl) between a numerical aperture NAill of an illuminationoptical system and a numerical aperture NApl of a projection opticalsystem when circular illumination is performed by the illuminationoptical system). The third method has a demerit that it is necessary tomeasure the image size and compare it with a reference table provided inadvance. The third method has other demerits that when an effectivelight source distribution is formed into a complicated shape instead ofa circular shape, a table compatible with this shape is necessary, andthat measuring the image size is insufficient to measure a complicatedspatial coherence distribution.

SUMMARY OF THE INVENTION

The present invention has been made in consideration of theabove-described situation, and has as its object to provide a techniquefor measuring, for example, spatial coherence with a simple arrangement.

One of the aspect of the present invention provides a measurementapparatus which measures spatial coherence in an illuminated planeilluminated by an illumination system, the apparatus comprising ameasurement mask which has at least three pinholes and is arranged onthe illuminated plane, a detector configured to detect an interferencepattern formed by lights from the at least three pinholes, and acalculator configured to calculate the spatial coherence in theilluminated plane based on a Fourier spectrum obtained byFourier-transforming the interference pattern detected by the detector.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the first embodiment ofthe present invention;

FIGS. 2A to 2C are views illustrating effective light sourcedistributions;

FIGS. 3A to 3C are views showing spatial coherences in the object planeof an optical system;

FIG. 4 is a view showing the schematic arrangement of a measurementapparatus according to a modification to the first embodiment of thepresent invention;

FIG. 5 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the second embodiment ofthe present invention;

FIG. 6 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the third embodiment ofthe present invention;

FIG. 7 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the fourth embodiment ofthe present invention;

FIG. 8 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the fifth embodiment ofthe present invention;

FIGS. 9A and 9B are views illustrating pinhole patterns;

FIGS. 10A and 10B are views illustrating other pinhole patterns;

FIGS. 11A to 11C are views illustrating the spatial coherencemeasurement positions;

FIG. 12 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the sixth embodiment ofthe present invention;

FIG. 13 is a view illustrating a pinhole pattern;

FIG. 14 is a view illustrating an interference pattern;

FIG. 15 is a view illustrating the Fourier spectrum of the interferencepattern;

FIG. 16 is a graph illustrating spatial coherence;

FIG. 17 is a view schematically showing a Yong interferometer; and

FIG. 18 is a view showing the principle of a shearing interferometer.

DESCRIPTION OF THE EMBODIMENTS

Preferred embodiments of the present invention will be described belowwith reference to the accompanying drawings. Note that the samereference numerals denote the same elements throughout the drawings, anda repetitive description thereof will not be given.

First Embodiment

FIG. 1 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the first embodiment ofthe present invention. This measurement apparatus is included in anexposure apparatus which projects the pattern of an original (alsocalled a mask or reticle) onto a substrate by a projection opticalsystem 30 to expose the substrate. Note that the original is arranged onthe object plane of the projection optical system 30, and the substrateis arranged on the image plane of the projection optical system 30. Theobject plane of the projection optical system 30 is also an illuminatedplane illuminated by an illumination optical system 12.

The measurement apparatus according to the first embodiment isconfigured to measure spatial coherence in the object plane of theprojection optical system 30. The exposure apparatus includes theprojection optical system 30, an original positioning apparatus forarranging an original on the object plane of the projection opticalsystem 30, a substrate positioning apparatus for arranging a substrateon the image plane of the projection optical system 30, and anillumination system 10 for illuminating the original arranged on theobject plane (the illuminated plane). The measurement apparatus includesa measurement mask 20 arranged on the object plane of the projectionoptical system 30, and a detector 40 arranged on the image plane of theprojection optical system 30. The measurement mask 20 is typicallypositioned by the original positioning apparatus. The detector 40 istypically positioned by the substrate positioning apparatus.

The illumination system 10 illuminates the original during substrateexposure, and illuminates the measurement mask 20 during spatialcoherence measurement. The illumination system 10 includes, for example,a light source unit 11 and the illumination optical system 12. A lightsource unit for spatial coherence measurement can be the same as thatfor substrate exposure. Accordingly, a single light source unit 11 canbe used for both substrate exposure and spatial coherence measurement.Although the light source unit 11 can be, for example, an ArF excimerlaser having an oscillation wavelength of about 193 nm, a KrF excimerlaser having an oscillation wavelength of about 248 nm, or an EUV lightsource having a wavelength of about 13.5 nm, it is not limited to theseexamples. The illumination optical system 12 is configured toKohler-illuminate the original and the measurement mask 20. Theillumination optical system 12 includes, for example, a fly-eye lens,aperture stop, condenser lens, and slit, and has a function of forming atargeted effective light source shape (to be described later).

The measurement mask 20 has a plurality of pinholes 21. Herein, thepinhole means a through hole in a narrow sense. However, throughout thisspecification and the scope of claims, the pinhole includes a smalllocal region on the entire surface of a reflection type measurement maskconfigured to reflect only light which enters the local region.

The detector 40 detects (senses) an interference pattern formed on theimage plane of the projection optical system 30 by light emerging fromthe plurality of pinholes 21 in the measurement mask 20. The detector 40includes a photoelectric conversion device. Although the detector 40preferably includes an image sensor such as a CCD image sensor as aphotoelectric conversion device, it may include a unit-pixelphotoelectric conversion device or a linear sensor such as a CCD linearsensor. If a unit-pixel photoelectric conversion device or a linearsensor such as a CCD linear sensor is used as a photoelectric conversiondevice, the detector 40 can sense an interference pattern by scanningit.

If the spatial coherence of light with which the illumination system 10illuminates the original is relatively high, the exposure apparatuscannot transfer the original pattern onto the substrate because lightbeams having passed through the original pattern interfere with eachother. To avoid this situation, the spatial coherence of light whichilluminates the original is decreased using, for example, a fly-eyelens. The measurement apparatus is configured to measure spatialcoherence in the plane on which the original is arranged in the exposureapparatus.

The illumination optical system 12 forms effective light sourcedistributions having, for example, an annular shape (FIG. 2A), aquadrupole shape (FIG. 2B), and a dipole shape (FIG. 2C) using anaperture and a CGH (Computer Generated Hologram).

The relationship between illumination by the illumination system andspatial coherence in the object plane of the projection optical system,and particularly that between the effective light source distributionand spatial coherence in the object plane of the projection opticalsystem, will be explained below.

Let λ be the wavelength of light emitted by the light source unit 11, fbe the focal length of the illumination optical system 12, (ε, η) be thecoordinate position normalized by fλ, u(ε, η) be the effective lightsource distribution, and (x, y) be the coordinate position of themeasurement mask 20. Then, the distribution of spatial coherence (aso-called mutual intensity Γ(x, y)) at the origin (0, 0) is describedby:

Γ(x, y)=∫u(ε, η)exp{i2π(εx+ηy)}dεdη  (1)

Note that equation (1) is called the Van Cittert-Zernike theorem, whichindicates that spatial coherence is calculated by Fourier-transformingan effective light source distribution. When the measurement mask 20 isilluminated with an effective light source distribution having, forexample, an annular shape (FIG. 2A), a quadrupole shape (FIG. 2B), or adipole shape (FIG. 2C) while the amount of light is constant, spatialcoherence on the measurement mask 20 is as shown in FIGS. 3A, 3B, or 3C,respectively. Also, since the measurement mask 20 is Kohler-illuminatedas mentioned above, the spatial coherence described by equation (1)holds over the entire illumination region on the measurement mask 20 intheory.

The explanation will be continued assuming that the number of pinholes21 which are formed on the measurement mask 20 and serve to measurespatial coherences is three hereinafter. Assume that the three pinholes21 align themselves on one straight line at unequal intervals, and theirpositions are P0(x₀, y₀), P1(x₁, y₁), and P2(x₂, y₂), respectively, andsatisfy:

$\begin{matrix}{{y_{2} = {\frac{\left( {y_{1} - y_{0}} \right)\left( {x_{2} - x_{0}} \right)}{x_{1} - x_{0}} + y_{0}}}{{{x_{1} - x_{0}}} \neq {{x_{2} - x_{0}}}}{{{x_{1} - x_{0}}} \neq {{x_{2} - x_{1}}}}{{{x_{2} - x_{0}}} \neq {{x_{2} - x_{1}}}}} & (2)\end{matrix}$

An interference pattern formed on the detection surface of the detector40 as light which illuminates the measurement mask 20 in theillumination system 10 and is transmitted through the three pinholes 21passes through the projection optical system 30 is described by:

I=A[3+2Γ₀₁ cos(kL ₀₁ ·X)+2Γ₃₂ cos(kL ₀₂ ·X)+2Γ₁₂ cos(kL₁₂ ·X)]  (3)

where A is a proportionality constant, X is a vector representing thedetection position coordinates of the detector 40, Γ_(ij) is the spatialcoherence value at (x_(j)−x_(i), y_(j)−y_(i)) in the plane on which themeasurement mask 20 is arranged (the object plane), k is 2π/λ, L_(ij) isa vector which represents the difference between the optical pathlengths from Pi(x_(i), y_(i)) and Pj(x_(j), y_(j)) to the detectionposition of the detector 40 and is proportional to (x_(j)−x_(i),y_(j)−y_(i)), i and j are integers from 0 to 2, and X is the wavelengthof light emitted by the light source unit 11.

Fourier transformation is used to acquire the spatial coherencedistribution in the plane, on which the measurement mask 20 is arranged,based on the interference pattern detected by the detector 40. Acalculator 50 Fourier-transforms one interference pattern to calculatespatial coherences at a plurality of positions in the plane on which themeasurement mask 20 is arranged. If the interference pattern isdistorted due to the influence of the numerical aperture (NA) of theprojection optical system 30 in Fourier transformation, it is desirablyperformed after data interpolation by coordinate transformation whichtakes account of the NA. The Fourier transform of the interferencepattern described by equation (3) is given by:

$\begin{matrix}{{F\; F\; T\left\{ I \right\}} = {A\begin{bmatrix}{{3\; \delta \left( {0,0} \right)} + {\Gamma_{01}{\delta \left( \frac{1}{{kL}_{01}} \right)}} + {\Gamma_{02}{\delta \left( \frac{1}{{kL}_{02}} \right)}} +} \\{{\Gamma_{12}\left( \frac{1}{{kL}_{12}} \right)} + {\Gamma_{01}{\delta \left( {- \frac{1}{{kL}_{01}}} \right)}} +} \\{{\Gamma_{02}{\delta \left( {- \frac{1}{{kL}_{02}}} \right)}} + {\Gamma_{12}\left( {- \frac{1}{{kL}_{12}}} \right)}}\end{bmatrix}}} & (4)\end{matrix}$

This Fourier transformation yields a Fourier spectrum.

Let F₀ be the Fourier spectrum value around zero frequency, and F_(ij)be the Fourier spectrum value (although signals representing positiveand negative Fourier spectrum values are generated in the Fourier space,the absolute value of one of them is assumed to be F_(ij)) around afrequency corresponding to the difference in optical path length L_(ij)(the frequency of the interference pattern). Then, we can write:

F₀=3A

F_(ij)=Γ_(ij)A   (5)

From equation (5), we have:

$\begin{matrix}{\Gamma_{ij} = \frac{3F_{ij}}{F_{0}}} & (6)\end{matrix}$

In accordance with equation (6), the calculator 50 calculates thespatial coherence value Γ_(ij) at the position (x_(j)−x_(i),y_(j)−y_(i)) in the plane on which the measurement mask 20 is arranged.

When a measurement mask 20 having three pinholes 21 is used, the spatialcoherence values at three points (six points considering that thespatial coherence distribution is symmetric about the origin) areobtained by the above-mentioned calculation.

The interference pattern detected by the detector 40 is described by:

$\begin{matrix}{I \approx {{{\Gamma cos}\left( {\frac{2\pi \; {Xp}}{\lambda \; h}x} \right)} + {{Const}.}}} & (7)\end{matrix}$

where h is the distance between the focal position of the projectionoptical system 30 and the detection surface of the detector 40, X is themagnification of the projection optical system 30, and p is the distancebetween the pinholes 21 in the measurement mask 20.

In view of this, the detector 40 is set at a position at which thefrequency of the interference pattern does not exceed the Nyquistfrequency of the detector 40 and a sufficient light intensity isobtained. More specifically, the detector 40 is arranged at a positionwhich satisfies:

$\begin{matrix}{h > \frac{2{Xpg}}{\lambda}} & (8)\end{matrix}$

where g is the detection pitch of the detector 40.

The detector 40 may be a detector which measures the depth of an imageformed on a resist by exposing it, instead of using a photoelectricconversion device which detects the interference pattern itself.

Also, the calculator 50 may adjust the illumination system 10 based onthe spatial coherence measurement result. That is, the calculator 50 mayfeed back the spatial coherence measurement result to the illuminationsystem 10.

An optical system such as the projection optical system 30 is notindispensable, and an arrangement as illustrated in FIG. 4 may beadopted. In this case, the detector 40 is arranged at a position whichsatisfies equation (8). Note that X=1 and h is the distance between themeasurement mask 20 and the detector 40. The measurement mask 20 and thedetector 40 may be integrated with each other. Alternatively, themeasurement mask 20 may have a configuration which is insertable andexchangeable with respect to the detector 40.

As described above, according to the first embodiment, the measurementapparatus has a simple arrangement and yet can easily and accuratelymeasure spatial coherence in the plane, on which the original isarranged, in a short period of time.

Second Embodiment

FIG. 5 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the second embodiment ofthe present invention. This measurement apparatus uses a measurementmask 20 a. Note that details which are not particularly referred toherein can be the same as in the first embodiment. The measurement mask20 a has three pinholes 21 a which are not on one straight line. Thepositions of the three pinholes 21 a are assumed to be Pa0 (x_(a0),y_(a0)), Pa1 (x_(a1), y_(a1)), and Pa2 (x_(a2), y_(a2)) herein.

An interference pattern formed on the detection surface of a detector 40as light which illuminates the measurement mask 20 a in an illuminationsystem 10 and is transmitted through the three pinholes 21 a passesthrough a projection optical system 30 is described by:

I _(a) =A _(a)[3+2Γ_(a01) cos(kL _(aC1) ·X)+2Γ_(a02) cos(kL _(a02)·X)+2Γ_(a12) cos(kL _(a12) ·X)]  (9)

where Γ_(aij) is the spatial coherence value at (x_(aj)−x_(ai),y_(aj)−y_(ai)) in the plane on which the measurement mask 20 a isarranged, L_(aij) is a vector which represents the difference betweenthe optical path lengths from Pai (x_(ail , y) _(ai)) and Paj (x_(aj),y_(aj)) to the detection position of the detector 40 and is proportionalto (x_(aj)−x_(ai), y_(aj)-y_(ai)), and i and j are integers from 0 to 2.

A calculator 50 analyzes the interference pattern detected by thedetector 40 to calculate spatial coherence, as in the first embodiment.The analysis method will be explained below. The calculator 50Fourier-transforms the interference pattern detected by the detector 40.The Fourier transform of the interference pattern is given by:

$\begin{matrix}{{F\; F\; T\left\{ I_{a} \right\}} = {A_{a}\begin{bmatrix}\begin{matrix}{{3{\delta \left( {0,0} \right)}} + {\Gamma_{a\; 01}\delta \left( \frac{1}{{kL}_{a\; 01}} \right)} +} \\{{\Gamma_{a\; 02}{\delta \left( \frac{1}{{kL}_{a\; 02}} \right)}} + {\Gamma_{a\; 12}\left( \frac{1}{{kL}_{a\; 12}} \right)} +} \\{{\Gamma_{a\; 01}{\delta \left( {- \frac{1}{{kL}_{a\; 01}}} \right)}} +}\end{matrix} \\{{\Gamma_{a\; 02}{\delta \left( {- \frac{1}{{kL}_{a\; 02}}} \right)}} + {\Gamma_{a\; 12}\left( {- \frac{1}{{kL}_{a\; 12}}} \right)}}\end{bmatrix}}} & (10)\end{matrix}$

This Fourier transformation yields a Fourier spectrum.

Let F_(a0) be the Fourier spectrum value around zero frequency, andF_(aij) be the Fourier spectrum value (although signals representingpositive and negative Fourier spectrum values are generated in theFourier space, the absolute value of one of them is assumed to beF_(aij)) around a frequency corresponding to the difference in opticalpath length L_(aij) (the frequency of the interference pattern). Then,we can write:

F_(a0)=3A_(a)

F_(aij)=Γ_(aij)A_(a)   (11)

From equation (11), we have:

$\begin{matrix}{\Gamma_{aij} = \frac{3F_{aij}}{F_{a\; 0}}} & (12)\end{matrix}$

In accordance with equation (12), the calculator 50 calculates thespatial coherence value Γ_(aij) at the position (x_(aj−x) _(a1),y_(aj)−y_(a1)) in the plane on which the measurement mask 20 a isarranged.

When a measurement mask 20 a having three pinholes 21 a is used, thespatial coherence values at three points (six points considering thatthe spatial coherence distribution is symmetric about the origin) areobtained by the above-mentioned calculation.

Third Embodiment

FIG. 6 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the third embodiment ofthe present invention. This measurement apparatus uses a measurementmask 20 b. Note that details which are not particularly referred toherein can be the same as in the first or second embodiment.

The measurement mask 20 b has four pinholes 21 b having differentrelative positions. The positions of the four pinholes 21 b are assumedto be Pb0 (x_(b0), y_(b0)), Pb1 (x_(b1), y_(b1)), Pb2 (x_(b2), y_(b2)),Pb3 (x_(b3), y_(b3)) herein. When two pinholes are present at positions(X₁, Y₁) and (X₂, Y₂), their relative position is (X₂−X₁, Y₂−Y₁).

An interference pattern formed on the detection surface of a detector 40as light which illuminates the measurement mask 20 b in an illuminationsystem 10 and is transmitted through the four pinholes 21 b passesthrough a projection optical system 30 is described by:

I _(b) =A _(b)└4+2Γ_(b01) cos(kL _(b01) ·X)+2Γ_(b02) cos(kL _(b02)·X)+2Γ_(b02) cos(kL _(b03) ·X)+2Γ_(b12) cos(kL _(b12) ·X)+2Γ_(b13)cos(kL _(b13) ·X)+2Γ_(b23) cos(kL _(b23) ·X)]  (13)

where Γ_(bij) is the spatial coherence value at (x_(bj)−x_(bi),y_(bj)−y_(bi)) in the plane on which the measurement mask 20 b isarranged, L_(bij) is a vector which represents the difference betweenthe optical path lengths from Pbi (x_(bi), y_(bi)) and Pbj (x_(bj),y_(bj)) to the detection position of the detector 40 and is proportionalto (x_(bj)−x_(bi), y_(bj)-y_(bi)), and i and j are integers from 0 to 3.

A calculator 50 analyzes the interference pattern detected by thedetector 40 to calculate spatial coherence. The analysis method will beexplained below. The calculator 50 Fourier-transforms the interferencepattern detected by the detector 40. The Fourier transform of theinterference pattern is given by:

$\begin{matrix}{{F\; F\; T \left\{ I_{b} \right\}} = {A_{b}\left\lbrack \begin{matrix}\begin{matrix}\begin{matrix}{{4{\delta \left( {0,0} \right)}} + {\Gamma_{b\; 01}{\delta \left( \frac{1}{{kL}_{{b0}\; 1}} \right)}} + {\Gamma_{b\; 02}{\delta \left( \frac{1}{{kL}_{b\; 02}} \right)}} +} \\{{\Gamma_{b\; 03}\left( \frac{1}{{kL}_{b\; 03}} \right)} + {\Gamma_{b\; 12}\left( \frac{1}{{kL}_{b\; 12}} \right)} + {\Gamma_{b\; 13}\left( \frac{1}{{kL}_{b\; 13}} \right)} +} \\{{\Gamma_{b\; 23}\left( \frac{1}{{kL}_{b\; 23}} \right)} + {\Gamma_{b\; 01}{\delta \left( {- \frac{1}{{kL}_{b\; 01}}} \right)}} +} \\{{\Gamma_{b\; 02}{\delta \left( {- \frac{1}{{kL}_{b\; 02}}} \right)}} + {\Gamma_{b\; 03}\left( {- \frac{1}{{kL}_{b\; 03}}} \right)} +}\end{matrix} \\{{\Gamma_{b\; 12}\left( {- \frac{1}{{kL}_{b\; 12}}} \right)} + {\Gamma_{b\; 13}\left( {- \frac{1}{{kL}_{b\; 13}}} \right)} +}\end{matrix} \\{\Gamma_{b\; 23}\left( {- \frac{1}{{kL}_{b\; 23}}} \right)}\end{matrix} \right\rbrack}} & (14)\end{matrix}$

This Fourier transformation yields a Fourier spectrum.

Let F_(b0) be the Fourier spectrum value around zero frequency, andF_(bij) be the Fourier spectrum value (although signals representingpositive and negative Fourier spectrum values are generated in theFourier space, the absolute value of one of them is assumed to beF_(bij)) around a frequency corresponding to the difference in opticalpath length L_(bij) (the frequency of the interference pattern). Then,we can write:

F_(b0)=4A_(b)

F_(bij)=Γ_(bij)A_(b)   (15)

From equation (15), we have:

$\begin{matrix}{\Gamma_{bij} = \frac{4F_{bij}}{F_{b\; 0}}} & (16)\end{matrix}$

In accordance with equation (16), the calculator 50 calculates thespatial coherence value Γ_(bij) at the position (x_(bj)−x_(bi),y_(bj)−y_(bi)) in the plane on which the measurement mask 20 b isarranged.

When a measurement mask 20 b having four pinholes 21 b is used, thespatial coherence values at six points (12 points considering that thespatial coherence distribution is symmetric about the origin) areobtained by the above-mentioned calculation. This number applies to acase in which two out of four is selected.

As can easily be seen from the above-mentioned examples, the larger thenumber of pinholes, the larger the number of spatial coherencemeasurement points. More specifically, letting N be the number ofpinholes, the number of measurement points is N(N−1)/2. Note thatpinholes need to be arranged at positions at which the Fourier spectraof interference patterns each formed by light transmitted through twopinholes do not overlap each other. However, the same does not apply toa case in which pinholes are arranged at relatively the same position inorder to increase the light intensity of the interference pattern, aswill be described later.

Fourth Embodiment

FIG. 7 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the fourth embodiment ofthe present invention. This measurement apparatus uses a measurementmask 20 c. Note that details which are not particularly referred toherein can be the same as in the first, second, or third embodiment.

In the fourth embodiment, three pinholes 21 c in the measurement mask 20c have the same relative position in order to increase the lightintensity of an interference pattern formed on the detection surface ofa detector 40. The three pinholes 21 c are arranged at positions Pc0(x_(c0), y_(c0)), Pc1 (x_(c1), y_(c1)), and Pc2 (x_(c2), y_(c2)) whichalign themselves on one straight line. Note that x_(c2)=2x_(c1)−x_(c0)and y_(c2)=2y_(c1)−y_(c0). Note also that the relative position betweenPc0 and Pc1 is the same as that between Pc1 and Pc2.

An interference pattern formed on the detection surface of a detector 40as light which illuminates the measurement mask 20 c in an illuminationsystem 10 and is transmitted through the three pinholes 21 c passesthrough a projection optical system 30 is described by:

I _(c) =A _(c)[3+2Γ_(c01) cos(kL _(c01) ·X)+2Γ_(c02) cos(kL _(c02)·X)+2Γ_(c12) cos(kL _(c12) ·X)]  (17)

Since the relative position between Pc0 and Pc1 is the same as thatbetween Pc1 and Pc2, Lc01=Lc12. Also, since the three pinholes 21 c areadjacent to each other, Γ_(c01)=Γ_(c12). Under these conditions,equation (17) can be rewritten as:

I _(c) =A _(c)[3+4Γ_(c01) cos(kL _(c01) ·X)+2Γ_(c02) cos(kL _(c02)·X)]  (18)

As can be seen from equation (18), the frequency coefficient in the termof Γ_(c01) in this embodiment is twice that in the first embodiment. TheFourier transform of the interference pattern described by equation (18)is given by:

$\begin{matrix}{{F\; F\; T\left\{ I_{c} \right\}} = {A_{c}\begin{bmatrix}\begin{matrix}{{3{\delta \left( {0,0} \right)}} + {2\Gamma_{c\; 01}\delta \left( \frac{1}{{kL}_{c\; 01}} \right)} +} \\{{\Gamma_{c\; 02}{\delta \left( \frac{1}{{kL}_{c\; 02}} \right)}} + {2\Gamma_{c\; 01}{\delta \left( {- \frac{1}{{kL}_{c\; 01}}} \right)}} +}\end{matrix} \\{\Gamma_{c\; 02}{\delta \left( {- \frac{1}{{kL}_{c\; 02}}} \right)}}\end{bmatrix}}} & (19)\end{matrix}$

This Fourier transformation yields a Fourier spectrum.

Let F_(c0) be the Fourier spectrum value around zero frequency, andF_(c01) be the Fourier spectrum value (although signals representingpositive and negative Fourier spectrum values are generated in theFourier space, the absolute value of one of them is assumed to beF_(c01)) around a frequency corresponding to the difference in opticalpath length L_(c01) (the frequency of the interference pattern). Then,we can write:

F_(c0)=4A_(c)

F_(c01)=Γ_(c01)A_(c)   (20)

From equation (20), we have:

$\begin{matrix}{\Gamma_{c\; 01} = \frac{2F_{c\; 01}}{F_{c\; 0}}} & (21)\end{matrix}$

In accordance with equation (21), a calculator 50 calculates the spatialcoherence value Γ_(c01) at the position (x_(c1)−x_(c0), y_(c1)−y_(c0))in the plane on which the measurement mask 20 c is arranged.

The calculator 50 calculates Γ_(c02) in accordance equation (6), as inthe first embodiment.

In the fourth embodiment, the spatial coherence values at two points(four points considering that the spatial coherence distribution issymmetric about the origin) can be measured using three pinholes, andthe measured intensity of Γ_(c01) is twice that in the first embodiment,facilitating the measurement.

Fifth Embodiment

FIG. 8 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the fifth embodiment ofthe present invention. This measurement apparatus uses a measurementmask 20 d. Note that details which are not particularly referred toherein can be the same as in the first to fourth embodiments.

In the fifth embodiment, four pinholes 21 d in the measurement mask 20 dhave the same relative positions in order to increase the lightintensity of an interference pattern formed on the detection surface ofa detector 40. The four pinholes 21 d are arranged at positions Pd0(x_(d0), y_(d0)), Pd1 (x_(d1), y_(d1)), Pd2 (x_(d2), y_(d2)), and Pd3(x_(d3), y_(d3)) which correspond to the vertices of a parallelogram.Note that x_(d3)=x_(d2)+x_(d1)−x_(d0d) and y_(d3)=y_(d2)+y_(d1)−y_(d0).Note also that the relative position between Pd0 and Pd1 is the same asthat between Pd2 and Pd3, and the relative position between Pd0 and Pd2is the same as that between Pd1 and Pd3.

An interference pattern formed on the detection surface of the detector40 as light which illuminates the measurement mask 20 d in anillumination system 10 and is transmitted through the four pinholes 21 dpasses through a projection optical system 30 is described by:

I _(d) =A[4+2Γ_(d01) cos(kL _(d01) ·X)+2Γ_(d02) cos(kL _(d02)·X)+2Γ_(d03) cos(kL _(d03) ·X)+2Γ_(d12) cos(kL _(d12) ·X)+2Γ_(d13)cos(kL _(d13) ·X)+2Γ_(d23) cos(kL _(d23) ·X)]  (22)

where Γ_(dij) is the spatial coherence value at (x_(dj)−x_(di),y_(dj)−y_(di)) in the plane on which the measurement mask 20 d isarranged, L_(dij) is a vector which represents the difference betweenthe optical path lengths from Pdi (x_(di), y_(di)) and Pdj (x_(dj),y_(dj)) to the detection position of the detector 40 and is proportionalto (x_(dj)−x_(di), y_(dj)−y_(di)), and i and j are integers from 0 to 3.

Since the relative position between Pd0 and Pd1 is the same as thatbetween Pd2 and Pd3, and the relative position between Pd0 and Pd2 isthe same as that between Pd1 and Pd3, Γ_(d01)=Γ_(d23), L_(d01)=L_(d23),Γ_(d02)=Γ_(d13), and L_(d02)=L_(d13). Under these conditions, equation(22) can be rewritten as:

I _(d) =A└4+2Γ_(d01) cos(kL _(d01) ·X)+4Γ_(d02) cos(kL _(d02)·X)+2Γ_(d03) cos(kL _(d03) ·X)+2Γ_(d12) cos(kL _(d12) ·X)]  (23)

As can be seen from equation (23), the frequency coefficients in theterms of Γ_(d01) and Γ_(d02) in this embodiment are twice those in thethird embodiment.

The Fourier transform of the interference pattern described by equation(23) is given by:

$\begin{matrix}{{F\; F\; T\left\{ I_{d} \right\}} = {A\begin{bmatrix}\begin{matrix}\begin{matrix}{{4{\delta \left( {0,0} \right)}} + {2\Gamma_{d\; 01}{\delta \left( \frac{1}{{kL}_{d\; 01}} \right)}} + {2\Gamma_{d\; 02}\delta \left( \frac{1}{{kL}_{d\; 02}} \right)} +} \\{{\Gamma_{d\; 03}\left( \frac{1}{{kL}_{d\; 03}} \right)} + {\Gamma_{d\; 12}\left( \frac{1}{{kL}_{d\; 12}} \right)} +}\end{matrix} \\{{2\Gamma_{d\; 01}{\delta \left( {- \frac{1}{{kL}_{d\; 01}}} \right)}} + {\Gamma_{d\; 02}\delta \left( {- \frac{1}{{kL}_{d\; 02}}} \right)} +}\end{matrix} \\{{\Gamma_{d\; 03}\left( {- \frac{1}{{kL}_{d\; 03}}} \right)} + {\Gamma_{d\; 12}\left( {- \frac{1}{{kL}_{d\; 12}}} \right)}}\end{bmatrix}}} & (24)\end{matrix}$

This Fourier transformation yields a Fourier spectrum.

Let F_(d0) be the Fourier spectrum value around zero frequency, andF_(d01) and F_(d02) be the Fourier spectrum values (although signalsrepresenting positive and negative Fourier spectrum values are generatedin the Fourier space, the absolute values of one of them are assumed tobe F_(d01) and F_(d02)) around frequencies corresponding to thedifferences in optical path length L_(d01) and L_(d02) (the frequenciesof the interference patterns). Then, we can write:

F_(d0)=4A

F_(d01)=2Γ_(d01)A

F_(d02)=2Γ_(d02)A   (25)

From equation (25), we have:

$\begin{matrix}{{\Gamma_{d\; 01} = \frac{2F_{d\; 01}}{F_{d\; 0}}}{\Gamma_{d\; 02} = \frac{2F_{d\; 02}}{F_{d\; 0}}}} & (26)\end{matrix}$

In accordance with equation (26), a calculator 50 calculates the spatialcoherence values Γ_(d01) and Γ_(d02) at the positions (x_(d1)−x_(d0),y_(d1)−y_(d0)) and (x_(d2)−x_(d0), y_(d2)−y_(d0)) in the plane on whichthe measurement mask 20 d is arranged.

The calculator 50 calculates Γ_(d12) and Γ_(d03) in accordance withequation (16), as in the third embodiment.

In the fifth embodiment, the spatial coherence values at four points(eight points considering that the spatial coherence distribution issymmetric about the origin) can be measured using four pinholes, and themeasured intensities of Γ_(d01) and Γ_(d02) are twice those in the thirdembodiment.

It is also possible to further increase the light intensity of theinterference pattern, which is detected by the detector 40, using fouror more pinholes having the same relative positions. For example,pinholes can be two-dimensionally and periodically arranged as shown inFIGS. 9A and 9B. With this arrangement, the interference pattern becomesrobust against disturbances such as noise as its light intensityincreases, thus improving the measurement accuracy and facilitating themeasurement. FIG. 9A shows an example in which pinholes are arranged atthe intersections of first lines arrayed with equal spaces between themalong a first direction, and second lines arrayed with equal spacesbetween them along a direction perpendicular to the first direction.FIG. 9B shows an example in which pinholes are arranged at theintersections of first lines arrayed with equal spaces between themalong a first direction, second lines arrayed with equal spaces betweenthem along a second direction (the second direction forms an angle of60° with the first direction), and third lines arrayed with equal spacesbetween them along a third direction (the third direction forms an angleof 60° with both the first and second directions).

The calculator 50 can calculate spatial coherence Γ_(p) in accordancewith:

$\begin{matrix}{\Gamma_{p} = \frac{2{NF}_{p}}{N_{p}F_{0}}} & (27)\end{matrix}$

where N is the total number of pinholes, N_(p) is the total number ofpinholes which contribute to form an interference pattern with afrequency v (one pair of pinholes is counted as two pinholes), F₀ is theFourier spectrum value of the interference pattern around zerofrequency, and F_(p) is the Fourier spectrum value around the frequencyv.

The intensity of an interference pattern with the frequency v isproportional to N_(p).

The use of a plurality of masks having pinholes with different relativepositions allows an increase in the number of spatial coherencemeasurement points. For example, when pinhole patterns as shown in FIGS.10A and 10B are used for the measurement, the measurement positions areas shown in FIGS. 11A and 11B. Hence, the positions of the obtainedspatial coherences are as shown in FIG. 11C, revealing that the numberof measurement points increases and the density of measurement positionsincreases in turn.

The arrangement of pinholes may be determined by determining themeasurement points in accordance with the effective light sourcedistribution in the illumination optical system.

The number of measurement points can also be increased by measuring theinterference pattern while changing the relative position betweenpinholes by rotating or moving the measurement mask. This measurementapparatus can include a driving mechanism which rotates or moves themeasurement mask.

Sixth Embodiment

FIG. 12 is a view showing the schematic arrangement of a measurementapparatus and exposure apparatus according to the sixth embodiment ofthe present invention. This measurement apparatus is included in anexposure apparatus so as to measure σ in an exposure apparatus. Thismeasurement apparatus uses a measurement mask 20 e. Note that detailswhich are not particularly referred to herein can be the same as in thefirst to fifth embodiments.

σ is the ratio (NAill/NApl) between a numerical aperture NAill of anillumination optical system 12 and a numerical aperture NApl of aprojection optical system 30 when a circular region is illuminated bythe illumination optical system 12. When the measurement mask 20 e isKohler-illuminated with a circular effective light source distributionhaving the numerical aperture NAill, spatial coherence is given by:

$\begin{matrix}{{{\Gamma (r)} = \left\lbrack \frac{2{J_{1}(R)}}{R} \right\rbrack}{R = \frac{2\pi \; {rNAill}}{\lambda}}} & (28)\end{matrix}$

where r is the distance from a reference point, J₁ is a first-orderBessel function. Note that Γ is normalized for a value r=0.

Assuming that spatial coherence has point symmetry, pinholes in themeasurement mask 20 e can be arranged at positions obtained by almostlinearly changing the distances and angles between the pinholes, asillustrated in FIG. 13, in order to measure Γ in equation (28). In FIG.13, when four pinholes are indicated by Q1, Q2, Q3, and Q4, thedistances between Q1 and Q2, Q1 and Q3, Q1 and Q4, Q2 and Q3, Q2 and Q4,and Q3 and Q4 are R, 1.5R, 2R, 1.25R, 2.55R, and 1.7R, respectively.

At this time, an interference pattern formed on the detection surface ofa detector 40 by light transmitted through the pinholes is as shown inFIG. 14, and has a Fourier spectrum as shown in FIG. 15. In FIG. 15, theFourier spectrum is indicated by the logarithm of an absolute value.

Fourier spectrum signals S1 to S6 represent that light beams transmittedthrough Q1 and Q2, Q1 and Q3, Q1 and Q4, Q2 and Q3, Q2 and Q4, and Q3and Q4 interfere with each other on the detection surface of thedetector 40 with certain spatial coherence. The values of the Fourierspectrum signals S1 to S6 depend on the magnitude of spatial coherence.

A calculator 50 can calculate spatial coherence in accordance withequation (9) using the signals S1 to S6 shown in FIG. 15, as in thethird embodiment. This makes it possible to obtain spatial coherence Γwhich depends only on the distance, as shown in FIG. 16. The calculator50 can calculate σ from the value of Γ. Measurement points lie along theabove-mentioned distances, that is, r=R, 1.5R, 2R, 1.25R, 2.55R, and1.7R herein.

Seventh Embodiment

In the seventh embodiment of the present invention, a function ofcontrolling the illumination system 10 is added to the calculators 50 inthe first to sixth embodiments. The calculator 50 not only calculatesspatial coherence obtained in the above-mentioned way, but also servesas a controller which controls the effective light source distributionin the illumination system 10 based on the spatial coherence.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2008-124971, filed May 12, 2008, which is hereby incorporated byreference herein in its entirety.

1. A measurement apparatus which measures spatial coherence in anilluminated plane illuminated by an illumination system, the apparatuscomprising: a measurement mask which has at least three pinholes and isarranged on the illuminated plane; a detector configured to detect aninterference pattern formed by lights from said at least three pinholes;and a calculator configured to calculate the spatial coherence in theilluminated plane based on a Fourier spectrum obtained byFourier-transforming the interference pattern detected by said detector.2. The apparatus according to claim 1, wherein said calculatorcalculates a ratio between a value of the Fourier spectrum around zerofrequency and a value of the Fourier spectrum around a frequency of theinterference pattern to calculate the spatial coherence in theilluminated plane.
 3. The apparatus according to claim 1, wherein saidcalculator calculates spatial coherence Γ_(p) in accordance with:$\Gamma_{p} = \frac{2{NF}_{p}}{N_{p}F_{0}}$ where N is the totalnumber of pinholes of said measurement mask, N_(p) is the total numberof pinholes which contribute to form an interference pattern with afrequency v of the detected interference pattern, F₀ is a value of theFourier spectrum around zero frequency, and F_(p) is a value of theFourier spectrum around the frequency v.
 4. The apparatus according toclaim 1, wherein said at least three pinholes include three pinholesarranged at unequal intervals.
 5. The apparatus according to claim 1,wherein said at least three pinholes include three pinholes which arenot on one straight line.
 6. The apparatus according to claim 1, whereinsaid at least three pinholes include pinholes arranged so as to increasea light intensity of the interference pattern formed on the illuminatedplane.
 7. The apparatus according to claim 1, further comprising adriving mechanism configured to drive said measurement mask.
 8. Theapparatus according to claim 1, wherein a wavelength λ of light whichilluminates the illuminated plane, an interval p between said pinholes,a distance h between said measurement mask and said detector, and adetection pitch g of said detector satisfy: $h > \frac{2{pg}}{\lambda}$9. The apparatus according to claim 1, wherein said pinholes in saidmeasurement mask are arranged at positions obtained by substantiallylinearly changing the interval between said pinholes and a direction inwhich said pinholes are arranged.
 10. An exposure apparatus whichilluminates an original by an illumination system, and projects apattern of the original onto a substrate by a projection optical systemto expose the substrate, said apparatus comprising: a measurementapparatus configured to measure spatial coherence in an illuminatedplane illuminated by the illumination system, said measurement apparatuscomprising: a measurement mask which has at least three pinholes and isarranged on the illuminated plane; a detector configured to detect aninterference pattern formed by lights from said at least three pinholes;and a calculator configured to calculate the spatial coherence in theilluminated plane based on a Fourier spectrum obtained byFourier-transforming the interference pattern detected by said detector.11. The apparatus according to claim 10, wherein an effective lightsource distribution in the illumination system is controlled based onthe spatial coherence measured by said measurement apparatus.